I have just proven the following two new theorems:
Theorem Composition of complete reloids is complete.
Theorem $latex (\mathsf{RLD})_{\mathrm{out}} g \circ (\mathsf{RLD})_{\mathrm{out}} f = (\mathsf{RLD})_{\mathrm{out}} (g \circ f)$ if $latex f$ and $latex g$ are both complete funcoids (or both co-complete).
See this note for the proofs.